1. Architectural Acoustics

2. Looking a bit deeper … Sound waves in 3D
Wave reflection and transmission
Wave interference and diffraction
How sound behaves in large spaces
Reflection
Absorption
Reverberation
Designing concert halls, listening rooms and other acoustic spaces – some considerations

3. Sound Reflection, Refraction, Absorption and Diffraction
Always reflect when they encounter a barrier (more precisely and impedance change) and follow the law of reflection: angle of reflection equals angle of incidence
Waves refract (“bend” or change direction) when they enter a medium in which their speed changes
Angles are always measured with respect to the normal or perpendicular

4. Call of the Loon (and other acoustic illusions!)
Air warms as you get above water surface
Cool air at water surface

5. The intensity of a reflected sound depends on the absorptivity of the reflecting surface

6. Consider a 500 Hz sound: I = 85 dB, Ireflected = (1-0.7)I
Example…
A choir in rehearsal in an empty hall produces an average SPL of 85 dB at the middle of the auditorium.
Estimate how the sound will change when the hall is full.
Consider a 500 Hz sound: I = 85 dB, Ireflected = (1-0.7)I So

7. Controlling Reflections…
More about this when we consider listening rooms and auditoriums

8. Reflection also depends on SHAPE
Convex shape disperses sound
Concave shape can focus sound

9. Resonant Modes in Rooms…
l = length, p = mode#
w = width, q = mode#
h = height, r = mode#
Link to a resonant mode calculator

10. Example…. Let’s find some resonant modes in this classroom…
Ignore the w and h modes for the moment
𝑓= 𝑣 𝑠 2 𝑝 𝑙 , p = 1,2,3…
L = 10 m; vs = 344 m/s…plug in the numbers
f = 17.2(p) Hz, therefore some resonant modes are…
F = 17.2, 34.4, 51.6, 68.8, 86.1, … Hz

11. Wave Diffraction and Interference
When waves either reflect or pass through small openings some interesting things happen!
This is why higher frequencies are much more directional than low frequencies

12. Wave Interference and Path Difference
When 2 waves travel slightly different distances (path difference) to get to your ear this introduces a relative shift in their phase
If the path difference is:
A whole number of waves the waves are still in phase and they add (constructive interference = ANTINODE)
An odd half multiple path difference leads to waves cancelling (destrucitve interference = NODE)

13. Diffraction Around Edges…
Low pitch sounds spread out more – “bend around corners”
High pitch sounds are more directional

14. Reverberation
Reverberation time is defined as the time required for a sound level to drop by 60dB
Often this is denoted RT60
Reverberation time depends on room volume and absorptivity/reflectivity of room surfaces
Figure shows “good”RT60 values for various room types

15. How Calculate and Measure RT60
Wallace Sabine – the Sabine Formula
𝑅𝑇 60 =(0.16 s/m) 𝑉 𝑆 𝑒
V = volume of room (m3) and Se = effective absorbing area
𝑆 𝑒 = 𝑎 1 𝑆 1 + 𝑎 2 𝑆 2 + 𝑎 3 𝑆 3 +…
Measure RT60 by noting time for a sound level to decay by 60 dB
Sound created by me clapping in my office. Top scale is in seconds

16. Tour the Jack Singer Hall in Calgary

17. Standards for “Good” Acoustics:
Clarity
little overlap of sounds
Uniformity
sound from all directions
Envelopment
everywhere the same
Smoothness
no echoes
Reverberation
appropriate length of time
Performer satisfaction
reflected to stage
Freedom from noise
no competition